Investigation of peak frequencies in the flopping regime with a two-cylinder array

The variation of the base pressure coefficient (C_p), velocity power spectra, and velocity time–frequency plots for an array of two cylinders aligned normal to the flow are presented. Power spectra of the fluctuating velocity downstream of the two-cylinder array with s/d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) show two peaks. The corresponding Wigner–Ville frequency–time plot of the same fluctuating velocity time series shows that the peak frequency observed during a narrow wake remains constant and relatively high while the peak frequency observed during a wide wake remains constant and relatively low. The two frequency values are consistent with the peaks observed in the power spectra. Thus, during flopping, the high frequency observed in the velocity power spectra is always the peak frequency for a narrow wake and the low frequency observed in the velocity power spectra is always the peak frequency for a wide wake.     

Flow past a circular cylinder over a free surface: Interaction between the near wake and the free surface deformation

Air-flow around a circular cylinder placed above a free surface and liquid flow under the free surface were investigated experimentally in a wind/wave tunnel. The cylinder spanned the tunnel test-section and was oriented normal to the freestream direction. The main objective of this study was to investigate the interaction of the cylinder wake with the free surface. The flow structure was analyzed for various gap widths, H, between the cylinder and the free surface using a digital particle image velocimetry (PIV) system with a spatial resolution of 2048×2048 pixels. The Reynolds number based on the cylinder diameter was 3.3×10³. For each experimental condition, 400 instantaneous velocity fields were measured and ensemble-averaged to obtain spatial distributions of the mean velocity and turbulence statistics. The results showed that the cylinder near-wake inclined upward due to the influence of the free surface elevation. Vortices were shed, even at a small gap ratio of H/D=0.25, where D is the cylinder diameter. Strong jet-like flow appeared in the gap beneath the cylinder. At a gap ratio of H/D=0.50, the jet flow exhibited a quasi-periodic vibration with a period of 2–3 s. The free surface deformation was caused by the pressure difference in the air-flow immediately above it. As the gap ratio increased, the inclination angle of the wake and the height of the free surface elevation decreased gradually. The liquid flow under the free surface followed a convective flow motion, and the range of the convection depended on the gap width between the cylinder and the free surface.     

Steady flow past a torus with aspect ratio less than 5

Steady flow past a torus with an aspect ratio less than 5 and its axis aligned with the flow is studied numerically by solving the steady, axisymmetric Navier–Stokes equations. The wake structure behind tori exhibits diverse behaviours. The detached recirculating zone on the axis, the attached recirculating zone, and the detached recirculating zone behind the torus tube may appear individually or concurrently, depending on the aspect ratio and the Reynolds number. A wake structure map is summarized based on the observed flow behaviours. Six flow regimes with different wake behaviours are identified and the corresponding flow regime map is plotted, which include the no-recirculating-zone regime, the single-detached-recirculating-zone regime, the single-attached-recirculating-zone regime, the two-recirculating-zone regime I, the two-recirculating-zone regime II, and the three-recirculating-zone regime. Over the range of aspect ratio 1.9<AR<2.4, the detached wake initially increases but then decreases in size with Reynolds number, and eventually disappears at Reynolds numbers beyond a critical value (depending on the aspect ratio). The underlying mechanisms of the onset and disappearance of the recirculating zones are discussed in terms of vorticity accumulation and base bleed. The recirculating zone first occurs when the maximum vorticity on the surface of the torus exceeds about 5. The detached recirculating zone on the axis of the torus disappears once the flow rate through the hole of the torus is beyond a certain threshold. In addition, the present results suggest that different transition modes to non-axisymmetric flow for tori with different aspect ratios reported in the literature may result from the wake structures prior to the transition.     

Influence of the orientation of a square cylinder on the wake properties

An experimental investigation of flow around a square cylinder placed at various angles with respect to the approach fluid velocity is reported. The focus of the study is toward examining the sensitivity of the wake properties to the cylinder orientation and Reynolds number. Angles of incidence in the range of 0-60° and Reynolds numbers of 1340, 4990, and 9980 have been considered. Velocity measurements have been carried out using an X-wire hotwire anemometer. The Strouhal number and the drag coefficient of the cylinder have been computed from the wake measurements. Utilizing the velocity traces at distinct probe locations in the near and the far wake, statistical properties such as the RMS velocities and the spectra have been obtained. Results obtained in the present work revealed that for a cylinder with zero inclination, flow separates from the corners on the face exposed to the incoming flow. For inclinations greater than zero, the points of separation on the cylinder move downstream and the wake size increases, but the separated shear layer rolls up over a shorter distance. These factors lead to a reduced drag coefficient and a higher Strouhal number. The center-line recovery of the time-averaged velocity and the decay rates of velocity fluctuations depend on the Reynolds number. A marginal effect of the cylinder orientation is also seen.     

Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder

The present work is aimed to give some insight into the relation between vortex shedding modes and transition to three-dimensionality in the wake of a freely vibrating cylinder by establishing a numerical model and analyzing the relevant results of two- and three-dimensional simulations. The compressible flow past an elastically-mounted cylinder is solved by using the immersed boundary method (IB method). The cylinder is free to vibrate in the transverse direction with zero structure damping. The response of displacement amplitude is studied with the variation of reduced velocity. Whether P+S mode exists in three-dimensional flow and the occurrence of 2P mode is caused by flow transition from two-dimensional to three-dimensional are problems of concern. Both 2P and P+S wake modes are observed in two- and three-dimensional simulations. The numerical results indicate that the flow transition from two-dimensional to three-dimensional is coupled with the cylinder vibration in the synchronization/lock-in regime. The wake formation given by three-dimensional simulations suggests that the P+S mode might exist in reality when the flow is reverted to two-dimensional by vortex induced vibration (VIV) at Re=300–350. When Reynolds number increases to 425, the wake formation undergoes transition to three-dimensionality and 2P mode is observed. The effect of mass ratio on the flow transition to three-dimensionality is studied. The relationship between wake modes and aerodynamic forces is discussed.     

ENERGY DISTRIBUTION IN MODES IN THE WAKE OF A FINITE-LENGTH CYLINDER BEFORE AND AFTER TRANSITION

The flow in the wake of a finite-length cylinder has been studied experimentally both before and after the transition to turbulence. This instability occurs at Reynolds numbers around 180–190. One end of the cylinder was fixed to the bottom of the test-section of a wind tunnel, whilst the other terminated in the open flow (free end). For these boundary conditions four main frequency modes within the wake can be identified. These are a centre-cell mode at the Strouhal frequency, end-cell modes with a frequency below the Strouhal frequency, a mode exhibiting the difference frequency between the centre-cell and end-cell modes, and a low-frequency mode (appearing only after transition to turbulence). In this work the energy content of these four modes has been determined throughout the wake, both before and after transition to turbulence. For three of the modes, the energy content is the same before and after transition, whereas the low-frequency mode exhibits energy two to four orders of magnitude greater after transition than before. Hence it is clear that the additional turbulence energy appearing in the wake after transition is located predominantly in this low-frequency mode. The appearance of this low-frequency mode is characterized by the simultaneous appearance of a peak in the power spectra of the velocity fluctuations centred about zero frequency (but with finite width). Consequently, the appearance of this zero frequency peak can be taken as the signature of the onset of turbulence. By considering the downstream growth rates of this low-frequency mode, evidence is presented which suggests that transition to turbulence may occur as a result of wake transition in the downstream central plane of the cylinder.     

Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Oblique impact by a spherical solid on a metal plate

The results of experimental studies of oblique impact by a spherical solid on a plane metal plate are presented. Plates made of AMTsM (plastic) and D16AT (rigid) alloys were used to determine the influence of the material characteristics on the impact aftereffects. The dependence of the ballistic limit on the angle of the impact velocity vector inclination to the plate plane was determined. The relationship between the ballistic limits of the oblique and normal impacts on the plate is established. The dependence of the ball motion trajectory refraction angles after collision with the plate on the ratio of the initial velocity to the ballistic impact is determined.     

Dependence of flow classification on the Reynolds number for a two-cylinder wake

This work aims to investigate the dependence of flow classification on the Reynolds number (Re) for the wake of two staggered cylinders. The Re examined ranges from 1.5×10³ to 2.0×10⁴. The pitch ratio, P^⁎=P/d examined is 1.2–6.0 (d is the cylinder diameter), and angle (α) is 0–90°, where P is the center-to-center spacing between two cylinders and α is the angle between the incident flow and the line through the cylinder centers. Two single hotwires were used to measure simultaneously the fluctuating streamwise velocities (u) in the vortex streets generated by the two cylinders. The power spectral density functions and the Strouhal numbers were then obtained from the u signals, based on which the flow structure pattern or mode could be determined. Over two hundred configurations of two staggered cylinders have been examined for each Re. It is found that Re has an appreciable effect on the dependence of the flow mode on P^⁎ and α. The observation is connected to the Re effect on the generic features of a two-cylinder wake such as flow separation, boundary layer thickness, gap flow deflection and vortex formation length.     

Wake structure of a finite circular cylinder of small aspect ratio

The wake of a finite circular cylinder of small aspect ratio was studied with a seven-hole probe and thermal anemometry. The cylinder was mounted normal to a ground plane and was partially immersed in a turbulent boundary layer. The time-averaged velocity and streamwise vorticity fields showed the development of the tip vortex structures, the extent of the near-wake recirculation zone, the downwash phenomenon and base vortex structures within the boundary layer. The wake structure and power spectra were similar for cylinder aspect ratios of 5 to 9, but a distinctly different behaviour was observed for an aspect ratio of 3.     

Large Eddy Simulation of Flow Control Around a Cube Subjected to Momentum Injection

The concept of Momentum Injection (MI) through Moving Surface Boundary layer Control (MSBC) applied to a cubic structure is numerically studied using Large Eddy Simulation at a Reynolds number of 6.7×10⁴. Two small rotating cylinders are used to add the momentum at the front vertical edges of the cube. Two configurations are studied with the yaw angle of 0° and 30°, respectively, with ratio of the rotation velocity of cylinders and the freestream velocity of 2. The results suggest that MI delays the boundary layer separation and reattachment, and thus reduces the drag. A drag reduction of about 6.2 % is observed in the 0° yaw angle case and about 44.1 % reduction in the 30° yaw angle case. In the case of 0° yaw angle, the main change of the flow field is the disappearance of the separation regions near the rotating cylinders and the wake region is slightly changed due to MI. In the 30° yaw angle case, the flow field is changed a lot. Large flow separations near one rotating cylinder and in the wake is significantly reduced, which results in the large drag reduction. Meanwhile, the yaw moment is increased about 50.5 %.     

截锥体头型弹丸低速斜入水实验研究

为研究截锥体头型弹丸在低速斜入水条件下，头部直径大小对入水空泡及弹道特性的影响，基于高速摄像方法，开展不同截锥体头型弹丸低速倾斜入水对比实验，得到了截锥体头弹丸头部直径大小对入水空泡、运动速度、俯仰角的影响规律。实验结果表明:截锥体头弹丸头部直径越大，尾部越早与空泡下壁面发生碰撞；头部直径大小对空泡深闭合时间几乎没有影响；弹丸空泡随头部直径增大而增大；头部直径过大或者过小均不利于入水稳定性；弹丸速度低于临界值时呈上升趋势，高于临界值时将呈现下降趋势。     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

Computations for a jet impinging obliquely on a flat surface

A SIMPLE-C algorithm and Jones-Launder k-ε two-equation turbulence model are used to simulate a two-dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.     

Three-component velocity field measurements of propeller wake using a stereoscopic PIV technique

A stereoscopic PIV (Particle Image Velocimetry) technique was used to measure the three-dimensional flow structure of the turbulent wake behind a marine propeller with five blades. The out-of-plane velocity component was determined using two CCD cameras with an angular displacement configuration. Four hundred instantaneous velocity fields were measured for each of four different blade phases, and ensemble averaged in order to find the spatial evolution of the propeller wake in the region from the trailing edge up to one propeller diameter (D) downstream. The influence of propeller loading conditions on the wake structure was also investigated by measuring the velocity fields at three advance ratios (J=0.59, 0.72 and 0.88). The phase-averaged velocity fields revealed that a viscous wake formed by the boundary layers developed along the blade surfaces. Tip vortices were generated periodically and the slipstream contracted in the near-wake region. The out-of-plane velocity component and strain rate had large values at the locations of the tip and trailing vortices. As the flow moved downstream, the turbulence intensity, the strength of the tip vortices, and the magnitude of the out-of-plane velocity component at trailing vortices all decreased due to effects such as viscous dissipation, turbulence diffusion, and blade-to-blade interaction.     

An aerodynamic wake in a hypersonic free-molecular gas flow

An experimental investigation was made of the form of an aerodynamic wake and the flow in it for the case where the flow is set up using a point source and is propagated in a motionless residual gas. It is shown that the geometry of the wake is determined by the mutual arrangement of the source and model, that the ground pressure is negligibly small, and that the flow in the wake is part of the oncoming flow, scattered by the residual gas. The value of the transverse velocity ratio exceeds by several orders of magnitude the value of the longitudinal ratio.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1976.     

Effect of Large Scale 3-D Structures on the Flow Around a Heated Cylinder at Low Reynolds Number

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as “mode E”. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of “mode E”, with the development of Λ-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.     

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn,buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.     

Flow Field Around Single and Tandem Piers

The present study provides a comparison between the flow pattern around two circular piers in tandem and a single pier set up on a moderately rough flat bed in a laboratory flume. Velocities are measured by an Acoustic Doppler Velocimeter (ADV). The contours of the time-averaged velocity components, Reynolds shear stresses, turbulence intensities and turbulence kinetic energy at different planes are presented. Streamlines and vectors are used to study the flow features. The analysis of power spectra around the piers is also presented. The results show that the presence of downstream pier changes the flow structure to a great extent, particularly in the near-wake region. Within the gap between the two piers, a stronger and substantial upflow is shaped. However, a weaker transverse-deflection is formed in comparison with that in the single pier. Near the bed, the velocity of flow approaching the downstream pier decreases to 0.2–0.3 times of the approach mean velocity (U ₀) due to the sheltering effect of the upstream pier. In the wake of downstream pier, the flow structure is completely different from the one in the wake of single pier. In comparison with the single pier, the values of turbulence kinetic energy and turbulence intensities show a considerable decrease around the tandem piers. In tandem piers, the high values of turbulence characteristics are found near the downstream pier. There is a recirculation zones just upstream of the sheltered pier close to the bed and another behind that pier near the free surface. The results show a decrease in the strength of vortical structure in the wake of tandem piers in comparison with single pier. It is shown that the formation of flow with different Reynolds number along the flow depth due to the effect of bed roughness, as well as pier spacing, can influence the type of flow regime of tandem case. In addition to enhancing the flow structure indulgence, the present detailed measurements can also be used for verification of numerical models.     

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.